What is the derivative of (x^{20}-22x+8e^x) ?

The derivative of (x^{20}-22x+8e^x) is e^xx^{20}+20e^xx^{19}-22e^xx-14e^x

What is the first derivative of (x^{20}-22x+8e^x) ?

The first derivative of (x^{20}-22x+8e^x) is e^xx^{20}+20e^xx^{19}-22e^xx-14e^x

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\frac{d}{d x} ((x^{20} - 22 x + 8) e^{x})

e^{x} x^{20} + 20 e^{x} x^{19} - 22 e^{x} x - 14 e^{x}

Solution steps

\frac{d}{d x} ((x^{20} - 22 x + 8) e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{20} - 22 x + 8, g = e^{x}

= \frac{d}{d x} (x^{20} - 22 x + 8) e^{x} + \frac{d}{d x} (e^{x}) (x^{20} - 22 x + 8)

\frac{d}{d x} (x^{20} - 22 x + 8) = 20 x^{19} - 22

\frac{d}{d x} (e^{x}) = e^{x}

= (20 x^{19} - 22) e^{x} + e^{x} (x^{20} - 22 x + 8)

Simplify

(20 x^{19} - 22) e^{x} + e^{x} (x^{20} - 22 x + 8) : e^{x} x^{20} + 20 e^{x} x^{19} - 22 e^{x} x - 14 e^{x}

= e^{x} x^{20} + 20 e^{x} x^{19} - 22 e^{x} x - 14 e^{x}

What is the derivative of (x^{20}-22x+8e^x) ?
The derivative of (x^{20}-22x+8e^x) is e^xx^{20}+20e^xx^{19}-22e^xx-14e^x
What is the first derivative of (x^{20}-22x+8e^x) ?
The first derivative of (x^{20}-22x+8e^x) is e^xx^{20}+20e^xx^{19}-22e^xx-14e^x